Properties

Label 3.13.as_fr_abai
Base Field $\F_{13}$
Dimension $3$
$p$-rank $3$
Does not contain a Jacobian

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Invariants

Base field:  $\F_{13}$
Dimension:  $3$
Weil polynomial:  $( 1 - 6 x + 13 x^{2} )^{3}$
Frobenius angles:  $\pm0.187167041811$, $\pm0.187167041811$, $\pm0.187167041811$
Angle rank:  $1$ (numerical)

Newton polygon

This isogeny class is ordinary.

$p$-rank:  $3$
Slopes:  $[0, 0, 0, 1, 1, 1]$

Point counts

This isogeny class does not contain a Jacobian, and it is unknown whether it is principally polarizable.

Point counts of the abelian variety

$r$ 1 2 3 4 5 6 7 8 9 10
$A(\F_{q^r})$ 512 4096000 10882013696 23887872000000 51681708060918272 112740186517737472000 247169660119103650167296 542801726578599395328000000 1192495236320772680785653842432 2619956699878396329300777472000000

Point counts of the (virtual) curve

$r$ 1 2 3 4 5 6 7 8 9 10
$C(\F_{q^r})$ -4 140 2252 29276 374876 4839020 62775212 815732156 10604160956 137856442700

Decomposition

1.13.ag 3

Base change

This is a primitive isogeny class.